Conten ts
Introduction
1. Year 3 review
1.1 Numbers
1.2 Algebra
1.3 Geometry
1.4 Probability and statistics
2. Year 3 extension
2.1 Classifying numbers and properties of numbers
2.2 Algebra extension
3. Relationships and functions
3.1 Relationships
3.2 Functions
4. Linear functions
4.1 Linear functions introduction
4.2 Graphing linear equations
4.3 Graphing linear inequalities
5. Systems of equations
5.1 Solving systems of equations by graphing
5.2 Solving systems of equations by substitution
5.3 Solving systems of equations by elimination
6. Matrices (online only)
7. Quadratic functions and equations
7.1 The graphs of y = x2 and y = ax2
7.2 Intersections of parabolas and straight lines
7.3 The graph of a quadratic function
7.4 Quadratic equations
8. Similarity
8.1 Similar shapes
8.2 Similar triangles
8.3 Similar triangles applications
9. Congruency
9.1 Equality and congruency
9.2 Congruent line segments
9.3 Congruent 2D shapes
10. Coordinate geometry
10.1 Distance and midpoint formulae
10.2 Transformations in the coordinate plane
10.3 Tessellations
11. Circle geometry
11.1 Circles review
11.2 Angle properties of circles
11.3 Chord properties of circles
11.4 Tangent properties of circles
11.5 Further circle properties
12. Trigonometry
12.1 Labelling triangles
12.2 The tangent ratio
12.3 The sine and cosine ratios
12.4 Exact values of the trigonometric ratios for 30 ͦ, 45 ͦ and 60 ͦ angles
12.5 Angles of elevation and depression
12.6 Bearings
13. Inverse functions, exponentials and logarithms
13.1 Inverse functions
13.2 Exponential functions y = ax
13.3 Logarithms and laws of logarithms
13.4 Logarithmic functions and equations
14. 3D geometry
14.1 Points, lines and planes in 3D
14.2 Polyhedra
14.3 Surface areas of prisms and cylinders
14.4 Surface areas of pyramids and cones
14.5 Surface area of a sphere
14.6 Volumes of prisms and cylinders
14.7 Volumes of cones, pyramids and spheres
15. Trigonometric equations and applications
15.1 Trigonometric ratios on the unit circle
15.2 Trigonometric relationships between acute and non-acute angles
15.3 The area of a triangle
15.4 The sine rule
16. Rational and irrational expressions and functions
16.1 Rational numbers and functions
16.2 Irrational numbers
17. Sequences and series
17.1 From patterns to generalisations
17.2 Series and sigma notation
17.3 Arithmetic sequences
17.4 Geometric sequences
18. Probability
18.1 Probability review
18.2 Combined events
19. Statistics
19.1 Collecting data
19.2 Organising and describing data
19.3 Representing and analysing data
19.4 Analysing bivariate data
20. Discrete mathematics
20.1 Graph theory review: graphs, subgraphs and trees
20.2 Weighted and directed graphs
20.3 Graph algorithms
20.4 Introduction to number theory
Answers
Index